The capability of the traction sheave of an elevator to transmit motion to the elevator hoisting ropes, as well as its capability to brake the rope, in other words, the grip between the traction sheave and the hoisting ropes, is substantially dependent on the length of the arc of contact between the hoisting ropes and the traction sheave and on the force with which the hoisting ropes are pressed against the traction sheave. In prior art, traction sheave elevator solutions are known in which the arc length used has been increased, e.g. by using a so-called Double Wrap roping arrangement or using an elevator car and counterweight of a relatively large weight in combination with the very common Single Wrap roping arrangement. In general, Double Wrap roping is used if it unreasonable to increase the weight of the hoisting cage and counterweight. For example, in fast elevators for a large hoisting height, it is more reasonable to improve the grip instead of increasing the moving masses. This type of fast elevators for a large hoisting height often also have compensating ropes or equivalent, which increase the weight of the moving masses while compensating the imbalance caused by the weight of the rope portions going to the elevator car and to the counterweight. In slower elevators designed for a lower hoisting height, a simple way of increasing the grip is to increase the weight of the car and counterweight. As a practical consequence of this, the starting points in the design of different elevators are very different and the final product ranges are at least to some degree non-uniform. Especially in slower elevators, relatively heavy elevator cars are needed even for small nominal loads.